Random signal sequences are sometimes injected into circuits. The randomness of the sequences may refer to the amplitude of the signals in the sequences, which may, for example, randomly vary between a set of discrete, predefined values. These sequences may be uncorrelated with the input signals to the circuits, i.e., the useful signals. The sequences may also be uncorrelated with each other. The sequences can be used for a variety of purposes, which are known in the art. For example, random sequences may be used to calibrate one or more stages of a pipelined analog-to-digital converter (ADC), e.g., to reduce a degree of mismatch between the devices in the stages or correct for non-linearity errors. Random sequences may also be used for dithering the input signal or for performing other types of calibrations. For convenience, these random or pseudo-random sequences will be referred to herein as “dither” signals, even though they may not be used to perform dithering in the traditional sense.
In a pipelined ADC, it may be desirable to remove the dither signals from the output of the ADC. This may be difficult because dither injected into one stage may propagate through subsequent stages, thereby influencing the signals output from one stage to the next, and may ultimately influence the overall output as well. Dither signals also experience the same gain effects as the input signals applied to the stages into which the dither is injected. Therefore, removal of the dither signals is not as straightforward as simply subtracting the dither injected into a stage from the output of that stage.
One method of removing dither signals from the output of the ADC is to correlate them out where they are used, by taking advantage of the lack of correlation between the dither signals. For example, if one sequence is used to calibrate stage 1 in a pipelined ADC, while other sequences are used to calibrate other stages, and/or to dither the pipeline, a correlation algorithm such as a Least Means Square (LMS) algorithm may be applied to correlate the overall output of the ADC with the sequence injected into stage 1 to determine a degree of correlation between the injected sequence and the overall output (which includes all the sequences). In a similar fashion, the degree of correlation between the sequences injected into other stages and the overall output may be determined. The output of each stage is then adjusted based on the degree of correlation for the respective stage so that, over time, the error attributed to the sequences is gradually reduced so that the sequences will average out to zero, while the intended sequence, i.e., the useful signal corresponding to the analog input of the ADC, remains. However, the convergence time of the correlation algorithm can be very long, even in the absence of any input signal, e.g., when the input is disconnected and only the random sequences are injected. This leads to long start-up times and long production test times, which can be prohibitive.
Accordingly, a need exists for methods of improving the convergence time of correlation algorithms in the context of injected dither signals.